On 3 Jan 2007, at 06:03, Ray Koopman wrote:
> Andrzej Kozlowski wrote:
>> Consider this list of 5 numbers:
>>
>> ls = Sort[Table[Random[], {5}]]
>> {0.165874, 0.256035, 0.556211, 0.811305, 0.865799}
>> Suppose we take epsilon = 0.3 and identify the numbers distant by
>> less than that from one another. Then
>>
>> Union[ls, SameTest -> (Abs[#1 - #2] < 0.3 &)]
>> {0.165874, 0.556211, 0.865799}
>> gives us just three numbers.
>> [...]
>> Note that when two numbers are identified it is the smaller one that
>> is kept.
>> [...]
>
> Is this just an observation, or official-but-not-publicly-documented?
> The arguments to SameTest seem always to be reverse-ordered (i.e.,
> #2 >= #1), even when the input list is unsorted, and the sequence of
> argument pairs seems to be the same regardless of whether the input
> list is sorted or unsorted. Can we conclude that Union sorts the input
> list before using SameTest, and that when SameTest returns True it is
> the second argument that is kept?
>
Yes, it is all true and actually I have known it fro a very long
time, so it is probably documented (but I can't check that right
now). Therefore there was no need to sort the list before running the
code and SameTest could be simply (#2-#1<0.3&). I suppose I faield
to think of that because I so used to working with spaces more
general the just the real line. The code will work, I think, with a
sequence of complex numbers (and Abs can even be replaced by Norm)
where we identify them if they are less than espilon apart in the
complex plane.
I have never tested how fast it is; probably not very fast, since
Union works much faster with the default value of SameTest (the same
is true for Sort which is much slower with a user defined ordering
function).
Andrzej Kozlowski